Problem: Reduce to lowest terms: $- \dfrac{9}{7} \div - \dfrac{9}{8} = {?}$
Solution: Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The reciprocal of $- \dfrac{9}{8}$ is $- \dfrac{8}{9}$ Therefore: $ - \dfrac{9}{7} \div - \dfrac{9}{8} = - \dfrac{9}{7} \times - \dfrac{8}{9} $ $ \phantom{- \dfrac{9}{7} \times - \dfrac{8}{9}} = \dfrac{-9 \times -8}{7 \times 9} $ $ \phantom{- \dfrac{9}{7} \times - \dfrac{8}{9}} = \dfrac{72}{63} $ The numerator and denominator have a common divisor of $9$, so we can simplify: $ \dfrac{72}{63} = \dfrac{72 \div 9}{63 \div 9} = \dfrac{8}{7} $